Is cos^2(x)=(1+cos(2x))/2 ?

The answer to whether cos^2(x)=(1+cos(2x))/2 is True

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prove cos^2(x)=(1+cos(2x))/2

prove

cos^{2} (x) = \frac{1 + cos ( 2 x )}{2}

True

Solution steps

cos^{2} (x) = \frac{1 + cos ( 2 x )}{2}

Manipulating right side

\frac{1 + cos ( 2 x )}{2}

Rewrite using trig identities

\frac{1 + cos ( 2 x )}{2}

Use the Double Angle identity:

cos (2 x) = 2 cos^{2} (x) - 1

= \frac{1 + 2 cos ^{2} ( x ) - 1}{2}

Simplify

\frac{1 + 2 cos ^{2} ( x ) - 1}{2} : cos^{2} (x)

\frac{1 + 2 cos ^{2} ( x ) - 1}{2}

1 + 2 cos^{2} (x) - 1 = 2 cos^{2} (x)

1 + 2 cos^{2} (x) - 1

Group like terms

= 2 cos^{2} (x) + 1 - 1

1 - 1 = 0

= 2 cos^{2} (x)

= \frac{2 cos ^{2} ( x )}{2}

Divide the numbers:

\frac{2}{2} = 1

= cos^{2} (x)

= cos^{2} (x)

= cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

p ro v e (csc^{2} (x) - 1) sec (x) = cot (x) csc (x)

p ro v e cot^{2} (y) (sec^{2} (y) - 1) = 1

p ro v e tan (x - \frac{π}{2}) = - cot (x)

p ro v e sin (π - θ) = sin (θ)

p ro v e tan (\frac{x}{2}) = csc (x) - cot (x)

Is cos^2(x)=(1+cos(2x))/2 ?
The answer to whether cos^2(x)=(1+cos(2x))/2 is True